## The First Six Books of the Elements of Euclid, in Which Coloured Diagrams and Symbols are Used Instead of Letters for the Greater Ease of learners.

London: William Pickering, 1847.

First edition, rare in the original publisher’s cloth, of “the most attractive edition of Euclid the world has ever seen” (Werner Oechslin, in an essay to the Taschen reprint, Cologne: 2010), in which colours are substituted for the usual letters to designate the angles and lines of geometric figures. Euclid’s *Elements* is the “oldest mathematical textbook still in common use today” (PMM), it “has exercised an influence upon the human mind greater than that of any other work except the Bible” (*DSB*); it is the only work of classical antiquity to have remained continuously in print, and to be used continuously as a textbook from the pre-Christian era to the 20th century. Written and designed to simplify Euclid’s propositions, Byrne’s remarkable example of Victorian printing is described by Rauri McLean as “one of the oddest and most beautiful books of the whole century” (*Victorian Book Design*, p. 70). The printing proved to be extremely difficult, requiring exact registration; only one thousand copies were originally published. After its exhibition at the Crystal Palace in 1851, Sparling remarked that “the application of colour printing for a didactic purpose was relatively uncommon … Colour wood engraving proved a difficult and expensive technique; by 1851 it was increasingly being supplanted by chromolithography” (*The Great Exhibition*, 137). The book has become the subject of renewed interest in recent years for its innovative graphic conception and its style which prefigures the modernist experiments of the Bauhaus and De Stijl movements. Euclid’s *Elements* is the only work of classical antiquity to have remained continuously in print, and to be used continuously as a textbook from the pre-Christian era to the 20th century. It is the foundation work not only for geometry but also for number theory. Euclid’s *Elements of Geometry* is a compilation of early Greek mathematical knowledge, synthesized and systematically presented by Euclid in ca. 300 BC. Books I-IV are devoted to plane geometry, Book V deals with the theory of proportions, and Book VI with the similarity of plane figures. *Provenance*: Small book label of Albert Sperisen on the paste-down and the signature of H. John Falk on the fly-leaf. SPERISON (1908-99), a well-known San Francisco printer, was the leading Eric Gill collector of the US. He later donated his Gill collection to the UCSF Library. Little is known about H. John Falk. He co-wrote the preface to Charles Howard Hinton's *A New Era of Thought* (1888) about the fourth dimension and its implications on human thinking, which was influenced by Plato, Kant, Gauss, and Lobachevsky, with Alicia Boole (the daughter of George Boole and sister-in-law of Hinton).

Born ca. 300 BC in Alexandria, Egypt, “Euclid compiled his *Elements* from a number of works of earlier men. Among these are Hippocrates of Chios (flourished *c.* 440 BC), not to be confused with the physician Hippocrates of Cos (*c.* 460–375 BC). The latest compiler before Euclid was Theudius, whose textbook was used in the Academy and was probably the one used by Aristotle (384–322 BC). The older elements were at once superseded by Euclid’s and then forgotten. For his subject matter Euclid doubtless drew upon all his predecessors, but it is clear that the whole design of his work was his own …

“Euclid understood that building a logical and rigorous geometry depends on the foundation—a foundation that Euclid began in Book I with 23 definitions (such as ‘a point is that which has no part’ and ‘a line is a length without breadth’), five unproved assumptions that Euclid called postulates (now known as axioms), and five further unproved assumptions that he called common notions. Book I then proves elementary theorems about triangles and parallelograms and ends with the Pythagorean theorem …

“The subject of Book II has been called geometric algebra because it states algebraic identities as theorems about equivalent geometric figures. Book II contains a construction of ‘the section,’ the division of a line into two parts such that the ratio of the larger to the smaller segment is equal to the ratio of the original line to the larger segment. (This division was renamed the golden section in the Renaissance after artists and architects rediscovered its pleasing proportions.) Book II also generalizes the Pythagorean theorem to arbitrary triangles, a result that is equivalent to the law of cosines. Book III deals with properties of circles and Book IV with the construction of regular polygons, in particular the pentagon.

“Book V shifts from plane geometry to expound a general theory of ratios and proportions that is attributed by Proclus (along with Book XII) to Eudoxus of Cnidus (*c.* 395/390–342/337 BC). While Book V can be read independently of the rest of the *Elements*, its solution to the problem of incommensurables (irrational numbers) is essential to later books. In addition, it formed the foundation for a geometric theory of numbers until an analytic theory developed in the late 19th century. Book VI applies this theory of ratios to plane geometry, mainly triangles and parallelograms, culminating in the ‘application of areas,’ a procedure for solving quadratic problems by geometric means” (Britannica).

“The significance of Euclid’s *Elements* in the history of thought is twofold. In the first place, it introduced into mathematical reasoning new standards of rigor which remained throughout the subsequent history of Greek mathematics and, after a period of logical slackness following the revival of mathematics, have been equaled again only in the past two centuries. In the second place, it marked a decisive step in the geometrization of mathematics … It was Euclid in his *Elements*, possibly under the influence of that philosopher who inscribed over the doors of the Academy ‘God is for ever doing geometry,’ who ensured that the geometrical form of proof should dominate mathematics. This decisive influence of Euclid’s geometrical conception of mathematics is reflected in two of the supreme works in the history of thought, Newton’s *Principia* and Kant’s *Kritik der reinen Vernunft*. Newton’s work is cast in the form of geometrical proofs that Euclid had made the rule even though Newton had discovered the calculus, which would have served him better and made him more easily understood by subsequent generations; and Kant’s belief in the universal validity of Euclidean geometry led him to a transcendental aesthetic which governs all his speculations on knowledge and perception. It was only toward the end of the nineteenth century that the spell of Euclidean geometry began to weaken and that a desire for the ‘arithmetization of mathematics’ began to manifest itself; and only in the second quarter of the twentieth century, with the development of quantum mechanics, have we seen a return in the physical sciences to a neo-Pythagorean view of number as the secret of all things. Euclid’s reign has been a long one; and although he may have been deposed from sole authority, he is still a power in the land” (*DSB*).

“Oliver Byrne’s most celebrated work, *The First Six Books of the Elements of Euclid in Which Coloured Diagrams and Symbols Are Used Instead of Letters for the Greater Ease of Learners,* was published in London by William Pickering in 1847. Byrne claimed to have conducted experiments showing that Euclid’s *Elements* could be mastered using this color method ‘in less than one third of the time usually employed.’ His expressed aim was ‘to teach people how to think and not what to think.’ In his final Royal Literary Fund application in 1880, Byrne wrote,

‘These works … have a greater aim than mere illustration; I do not introduce colours for the purpose of entertainment, or to amuse by certain combinations of tint and form, but to assist the mind in its researches after truth, to increase the facilities of instruction, and to diffuse permanent knowledge.’

“Byrne’s 1847 *Euclid* was one of the first multicolor printed books, and is today the most renowned and valuable of his works. Many consider it the most attractive edition of *Euclid’s Elements* ever produced. Byrne's *Euclid* was extremely difficult and expensive to produce, requiring exact registration of the pages in order to print each color, the typeface, and the vignettes; therefore, only one thousand copies were originally published. According to retired University College Dublin meteorology professor and mathematics blogger, Peter Lynch, the book was regarded as a curiosity, and was largely ignored; it did not sell well at a price of 25 shillings, almost five times the typical book price at the time.

“Historian of art and architecture Werner Oechslin, in his preface to the beautiful facsimile, *Oliver Byrne: The Elements of Euclid*, wrote that

‘no one who holds it in his hands can resist the fascination of its illustrations. The pictures are more captivating because they simply suggest, concretely demonstrate ad oculus and thus assist in the comprehension of mathematical laws that initially seem most difficult and abstract.’

“Byrne, according to Peter Lynch, ‘was not in the vanguard of mathematical thought.’ In Byrne’s time, Euclid's* Elements* was *the* geometry text used in British schools, but there was considerable debate about its suitability. Mathematicians such as Charles Dodgson (1832-1898), who wrote children's literature as Lewis Carroll, in his book *Euclid and His Modern Rivals* (1879), and Augustus De Morgan (1806-1871) debated how appropriate it was to teach Euclid's classical version of geometry versus a more modern approach. Byrne felt, as does Sid Kolpas, that geometry is the basis of all of mathematical science, and should provide a student's first formal experience with proof, the bedrock of mathematical thought.

“Written and designed purportedly to simplify Euclid’s geometry, Byrne's *Euclid* was an extraordinary example of Victorian printing and was described by typographer and book designer Ruari McLean in *Victorian Book Design and Colour Printing* as ‘one of the oddest and most beautiful books of the whole century.’ McLean described each page as

‘a unique riot of red, yellow and blue: on some pages letters and numbers only are printed in color, sprinkled over the pages like tiny wild flowers, demanding the most meticulous register; elsewhere, solid squares, triangles, and circles are printed in gaudy and theatrical colors, attaining a verve not seen again on book pages till the days of Dufy, Matisse and Derain.’

“McLean labeled Byrne’s work ‘… a decided complication of Euclid.’ Often, a pedagogical prophet is not recognized by his or her peers.

“Historian of mathematics and mathematics educator Florian Cajori (1859-1930) had a mixed opinion of the pedagogical approach of Byrne's *Euclid.* After asserting that the use of colored diagrams and symbols was ‘a noteworthy device for aiding the young mind through sensuous stimulus,’ he speculated that ‘the failure of the book is doubtless due to the want of moderation in the use of colors.’ David Eugene Smith (1860-1944), another historian of mathematics and mathematics educator, was also guarded in his opinion of Byrne's approach, stating that ‘[t]here is some merit in speaking of the red triangle instead of the triangle ABC, but not enough to give the method any standing.’ It is Sid Kolpas' opinion, in agreement with Cajori and Smith, that Byrne’s *magnum opus* is not well suited as a stand-alone geometry text, but is best used as a supplement to a geometry course, along with labeled diagrams, traditional proof, and algebraic argument; that way, it is not ‘a decided complication of Euclid,’ but rather an aid to better understanding Euclid's arguments. Mathematician Bill Casselman believes that while Byrne's *Euclid'*s ‘failures are interesting, … for students it has proved to be a fruitful source of projects.’ In fact, Kolpas has successfully used Byrne's work as a source of student projects, and as an inspiration for using color-coded diagrams within a traditional teaching approach.

“Contrary to McLean, Cajori, and Smith, Edward R. Tufte, pioneer in the visualization of data, indicated in his *Envisioning Information* that Byrne’s design may greatly clarify Euclid’s *Elements* for students with a visual preference for learning. That is, Byrne created a book that would help right-brained students master the complexities of geometry! Modern pedagogy teaches us that it is best to appeal to the visual, auditory, and kinesthetic senses when teaching mathematics. In the preface to his *Euclid,* Byrne stated that the traditional oral and written demonstrations of Euclid are enhanced by color dissections. To quote Byrne’s preface:

‘Sounds which address the ear are lost and die

In one short hour, but these which strike the eye,

Live long upon the mind, the faithful sight

Engraves the knowledge with a beam of light.’

“Byrne further indicated in his preface that he subscribed to the pedagogy of the Swiss educator Johann Heinrich Pestalozzi (1746-1827), considered by many to be the Father of Modern Education. Pestalozzi felt that education should be interactive and should appeal to all of the senses; the use of colored dissections enhances that appeal. It should be noted that Byrne’s *Euclid* was not his only attempt at using color and strongly visual explanations of mathematical concepts, similar to ‘proofs without words.’ In his *The Young Geometrician,* published in 1865, Byrne set out to teach geometric constructions with the use of color. Moreover, according to Ruari McLean in a letter to the second author, Byrne also intended to create a calculus text with the use of color dissections. The book was proofed, but never printed. Byrne indicated in the proof copy that the calculus text would be ‘uniform with The Coloured Euclid.’

“Byrne’s *The First Six Books of the Elements of Euclid in Which Coloured Diagrams and Symbols Are Used Instead of Letters for the Greater Ease of Learners* was designed and printed by the acclaimed printer Charles Whittingham (1795-1876) of the Chiswick Press. The book's use of color was its most striking feature, with equal angles, lines, or polygonal regions assigned the same bright primary color, and its colored shapes surely must have presented the greatest challenge to the printer. However, its more traditional black print was intricate and beautiful, too. Each proposition was set in black Caslon italic, with a beautifully engraved four-line initial vignette, usually an ‘I’ for ‘If’ or ‘In’. A four-line initial vignette therefore begins most pages in Byrne’s *Euclid.* Caslon is a group of beautiful serif typefaces designed by William Caslon (1692–1766). According to the Society of Printers, ‘It was at the Chiswick Press that the use of the old-face Caslon type was revived in 1843 … [A] revival followed by printers throughout England.’ At least three women assisted Whittingham: his daughters Charlotte and Elizabeth Whittingham studied art and calligraphy, and Mary Byfield turned their designs into beautiful wood engravings and made other contributions to the business as well. According to the *Dictionary of National Biography,*

‘Charlotte and Elizabeth were educated as artists, and from their designs came the greater part of the extensive collection of borders, monograms, head and tail pieces, and other embellishments still preserved and used. The engraver of most of the ornamental wood-blocks was Mary Byfield (d. 1871).’

“Byrne’s *Euclid* benefited from their beautiful work.

“According to Julie L. Mellby, graphic arts librarian at Princeton University, in her online article ‘Euclid in Color’, Byrne's *Euclid* was exhibited in London at the Great Exhibition of 1851. Praise was given for its beauty and the artistry of the printing, which may have influenced future publications and artwork. However, the book was sold for an extravagant price by contemporary standards, placing it out of the reach of educators who were supposed to make use of this new way of teaching geometry. Given the royal stamp on the upper right hand corner of the title page indicating ‘Sample: Department Of Science And Art,’ the second author suspects that his copy of Byrne's *Euclid* might have been a sample copy at the Great Exhibition” (https://www.maa.org/press/periodicals/convergence/oliver-byrne-the-matisse-of-mathematics-byrnes-euclid-geometry-understood-via-color-coded-diagrams).

Ing, *Whittingham Printer* 46; Keynes, *Pickering*, pp. 37, 65; McLean, *Victorian Book Design*, p. 70, illustration facing p. 53.

4to (232 x 187 mm), pp. xxix, [i], 268, illustrated throughout in three colours and black, printed in Caslon old-face type with ornamental initials by C. Whittingham of Chiswick. Original blue publisher’s cloth, spine with some very well done repairs.

Item #5516

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Price:
$19,500.00
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